Classifications

• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/55—Compression Theory, e.g. compression of random number, repeated compression
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F11/00—Error detection; Error correction; Monitoring
  • G06F11/07—Responding to the occurrence of a fault, e.g. fault tolerance
  • G06F11/08—Error detection or correction by redundancy in data representation, e.g. by using checking codes
  • G06F11/10—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/3068—Precoding preceding compression, e.g. Burrows-Wheeler transformation
  • H03M7/3077—Sorting
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/3084—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction using adaptive string matching, e.g. the Lempel-Ziv method
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/60—General implementation details not specific to a particular type of compression
  • H03M7/6005—Decoder aspects
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/60—General implementation details not specific to a particular type of compression
  • H03M7/6011—Encoder aspects
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/60—General implementation details not specific to a particular type of compression
  • H03M7/6035—Handling of unkown probabilities
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
  • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
  • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
  • H03M7/60—General implementation details not specific to a particular type of compression
  • H03M7/6064—Selection of Compressor
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
  • H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
  • H04N19/176—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a block, e.g. a macroblock
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/90—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using coding techniques not provided for in groups H04N19/10-H04N19/85, e.g. fractals

Definitions

• PCT/IB2017/050985 filed on 22 February 2017, and PCT/IB2017/053993 filed on 1 July 2017 submitted by the present inventor.
• This invention relates to the use of the concept and techniques revealed in the aforesaid four PCT Applications and improved on in the present Application, presenting a framework for ordering, organizing and describing digital data whether random or not for encoding and decoding purposes, including compression and decompression as well as encryption and decryption.
• the unity of invention lies in the description of the present Application revealing the invention of a framework CHAN FRAMEWORK for ordering, organizing and describing digital data that enables the development and use of coding schemes, methods and techniques under CHAN FRAMEWORK for the purpose of processing digital data for all kinds of use, including in particular the use in encryption/decryption and compression/decompression of digital data for all kinds of activities.
• One way of ordering and organizing digital data could be found in the present invention when revealing the relationship between different components of CHAN SHAPES (including CHAN RECTANGLES, CHAN TRAPESIA, CHAN SQUARES, CHAN TRIANGLE, CHAN LINE, CHAN DOT AND CHAN BARS or other shapes which describe the relations and characteristics of the basic components of the Processing Unit, a processing unit consisting of digital data in the form of binary bits) and the respective techniques in making coding (including encoding and decoding) of digital information for the use and protection of intellectual property, expressed in the form of digital information, including digital data as well executable code for use in device(s), including computer system(s) or computer- controlled device(s) or operating-system-controlled device(s) or system(s) that is/are capable of running executable code or using digital data.
• Such device(s) is/are mentioned hereafter as Device(s).
• this invention relates to the framework and method as well as its
• Storage Medium read-only or rewritable or volatile or non-volatile storage medium
• the Storage Medium such as physical memory or internal DRAM (Dynamic Random Access Memory) or hard disk or solid state disk (SSD) or ROM (Read Only Memory), or readonly or rewritable CD/DVD/HD-DVD/Blu-Ray DVD or hardware chip or chipset etc.
• the method of coding revealed, i.e. CHAN CODING, when implemented produces an encoded code, CHAN CODE that could be decoded and restored losslessly back into the original code; and if such coding is meant for compression, such compressed code could also be re-compressed time and again until it reaches its limit.
• this invention reveals a framework for creating an order for digital data so that digital data could be described and its characteristics could be investigated for the purpose of making compression / decompression or encryption / decryption of digital information.
• it makes possible the processing, storing, distribution and use of digital information in Device(s) connected over local clouds or internet clouds for the purpose of using and protecting intellectual property.
• the compressed code could not be restored correctly. If not used for compression purposes, the encoded code could be considered an encrypted code and using the correct corresponding decoding methods, such encrypted code could also be restored to the original code losslessly.
• CHAN CODING AND CHAN CODE including the concepts, methods, i.e. a combination of techniques, and techniques and the resultant code so produced as revealed in the aforesaid PCT Applications and in the present Application
• CHAN CODING AND CHAN CODE including the concepts, methods, i.e. a combination of techniques, and techniques and the resultant code so produced as revealed in the aforesaid PCT Applications and in the present Application
• PCT Applications and in the present Application could also be used in other scientific, industrial and commercial endeavors in various kinds of applications to be explored.
• the use of it in the Compression Field demonstrates vividly its tremendous use.
• application revealed in this invention are not limited to delivery or exchange of digital information over clouds, i.e. local area network or internet, but could be used in other modes of delivery or exchange of information.
• the present invention describes a novel method that could be used for making lossless data compression (besides also being suitable for use for the purpose of making encryption and losslessly decryption) and its restoration.
• Lossless data compression algorithms usually exploit statistical redundancy to represent data more concisely without losing information, so that the process is reversible. Lossless compression is possible because most real-world data has statistical redundancy. For example, an image may have areas of colour that do not change over several pixels; instead of coding "red pixel, red pixel, " the data may be encoded as "279 red pixels". This is a basic example of run-length encoding; there are many schemes to reduce file size by eliminating redundancy.
• LZ Lempel-Ziv
• DEFLATE is a variation on LZ optimized for decompression speed and compression ratio, but compression can be slow.
• DEFLATE is used in PKZIP, Gzip and PNG.
• LZW Lempel-Ziv-Welch
• LZR Lempel-Ziv-Renau
• LZ methods use a table-based compression model where table entries are substituted for repeated strings of data. For most LZ methods, this table is generated dynamically from earlier data in the input. The table itself is often Huffman encoded (e.g. SHRI, LZX).
• a current LZ-based coding scheme that performs well is LZX, used in Microsoft's CAB format.
• the class of grammar-based codes are gaining popularity because they can compress highly repetitive text, extremely effectively, for instance, biological data collection of same or related species, huge versioned document collection, internet archives, etc.
• the basic task of grammar-based codes is constructing a context-free grammar deriving a single string. Sequitur and Re-Pair are practical grammar compression algorithms for which public codes are available.
• Arithmetic coding invented by Jorma Rissanen, and turned into a practical method by Witten, Neal, and Cleary, achieves superior compression to the better-known Huffman algorithm and lends itself especially well to adaptive data compression tasks where the predictions are strongly context-dependent. Arithmetic coding is used in the bi-level image compression standard JBIG, and the document compression standard Dj Vu.
• the text entry system Dasher is an inverse arithmetic coder. [8]"
• the present invention presents a novel method, CHAN CODING that produces
• the additional information for one or more entries of the digital information is stored interspersed with the compressed data entries, how to differentiate the additional information from the original entries of the digital information is a problem and the separation of the compressed entries of the digital information during recovery presents another challenge, especially where the original entries of the digital information are to be compressed into different lengths and the additional information may also vary in length accordingly.
• the framework and method processes data correctly for the purposes of encryption/decryption or compression/decompression.
• the framework and method can be used for lossless data compression, lossless data encryption, and lossless decryption and restoration of the data.
• the framework makes no assumptions regarding digital data to be processed before processing the data
• the limit of compressing digital information as revealed by the present invention varies with the schema and method chosen by the relevant implementation in making compression, as determined by the size of the header used, the size of Processing Unit (containing a certain number of Code Units) or the size of Super Processing Units (containing a certain number of Processing Units) used as well as the size of un-encoded binary bits, which do not make up to a Processing Unit or Super Processing Unit. So this limit of compressing any digital information could be kept to just thousands of binary bits or even less depending on design and the nature of the relevant data distribution itself.
• CHAN FRAMEWORK AND CHAN CODING
• the random digital information to be compressed and recovered need not be known beforehand.
• CHAN FRAMEWORK will be defined in the course of the following description where appropriate. For instance, for a conventional data coder samples digital data using fixed bit size of 2 bits, it could always presents digital data in 2-bit format, having a maximum of 4 values, being 00, 01, 10 and 11, thus contrasting with the data coder under CHAN FRAMEWORK which uses the maximum number of data values that a data coder is designed to hold as the primary factor or criterion of data differentiation and bit size as non-primary factor or criterion amongst other criteria for data differentiation as well.
• the conventional data coders could be just one variant of data coder under CHAN FRAMEWORK; using the aforesaid conventional data coder using 2-bit format as an example, it could be put under CHAN FRAMEWORK, being a data coder having maximum number of values as 4 values (max4 class). So max4 class data coder under CHAN FRAMEWORK could have other variants such as being defined by the number of total bits used for all the unique 4 values as Bit Groups as well as further defined by the Head Type being used such as represented in Diagram 0 below: Diagram 0
• Max4 Class Primary Factor or Criterion for data differentiation
• CHAN FRAMEWORK AND LEGEND illustrating the concept of Processing Unit Components where a and b are two pieces of digital information, each representing a unit of code, Code Unit (being the basic unit of code of a certain number of binary bits of 0s and Is).
• Code Units represented by a certain number of binary bits of 0s and Is, is read one after another, for instance a is read as the first Code Unit, and b the second; a piece of digital information constitutes a Code Unit, and two such Code Units in Diagram 1 constitute a Processing Unit (the number of Code Units a Processing Unit contains could vary, depending on the schema and techniques used in the coding design, which is decided by the code designer and which could therefore be different from the case used in the present illustration using Diagram 1); for convenience and ease of computation, each Code Unit is best of equal definition, such as in terms of bit size for one cycle of coding process, using the same number scale without having to do scale conversion; consistency and regularity in encoding and decoding is significant to successfully recovery of digital information losslessly after encoding.
• Consistency and regularity in encoding and decoding means that the handling of digital information follows certain rules so that logical deduction could be employed in encoding and decoding in such ways that digital information could be translated or transformed, making possible alteration of data distribution such as changing the ratio of binary bits 0 and binary bits 1 of the digital information, and dynamic code adjustment (including code promotion, code demotion, code omission, and code restoration).
• rules for encoding and decoding are determined by the traits and contents of the Code Units or Processing Units or Super Processing Units and the associated schema, design and method of encoding and decoding used.
• Such rules or logic of encoding and decoding could be recorded as binary code inside the main header (for the whole digital data input) or inside a section header (of a section of the whole digital data input, which is divided into sections of binary bits) using binary bit(s) as indicators; and such binary code being indicators could also be embedded into the encoder and decoder where consistency and regularity of the schema, design and method of encoding and decoding allows;
• the Code Unit could be expressed and represented on any appropriate number scale of choice, including binary scale, octary, hexidecimal, etc.;
• the size of Code Unit, Code Unit Size could be of any appropriate choice of size, for instance on binary scale, such as 4 bits or 8 bits or 16 bits or 32 bits or 64 bits or any bit size convenient for computation could be used as Code Unit Size (the definition of Code Unit will be improved upon under CHAN FRAMEWORK beginning from Paragraph [54]);
• the digital number or value of each Code Unit represents the digital content of the Code Unit, the digital number signifying the bit signs of all the
• Diagram 2 Before encoding, the data of Diagram 2 is as in Diagram 1, assuming Code Unit Size of 64 bits, having a Processing Unit with two Code Units:
• RP Bit (1 bit), the first piece, the RP Piece of CHAN CODE and the combined value of a and b, A+B, (65 bits, i.e. 64 bits plus one, being bit size of the Code Unit Size plus one bit), i.e. the second piece, the Coded Value Piece or Content Value Piece (the CV Piece), of CHAN CODE makes up the resultant coded CHAN CODE, which also includes the associated header information, necessary for indicating the number of encoding cycles that has been carried out for the original digital information as well as necessary for remainder code processing.
• header information formation and processing has been mentioned in another PCT Patent Application, PCT/IB2015/056562, dated August 29, 2015 that has also been filed by the present inventor and therefore it is not repeated here.
• the CV piece could be further subdivided into sub-pieces when more Code Units are to be used according to schema and method of encoding and decoding so designed;
• RP Piece is a piece of code that represent certain trait(s) or characteristic(s) of the corresponding Code Units, representing the characteristics of Rank and Position between the two corresponding Code Units of a Processing Unit here.
• RP Piece is a subset of code to a broader category of code, which is named as Traits Code or Characteristics Code or Classification Code (so called because of the traits or the characteristics concerned being used to classify or group Code Units with similar traits or
• the CV Piece represents the encoded code of the content of one or more Code Units. Sometimes, depending on the schema and method of encoding and decoding, part of the content of the Code Units is extracted to become the Classification Code, so that what is left in the CV Piece is just the remaining part of content of the corresponding Code Units.
• the CV Piece constitutes the Content Code of CHAN CODE. So depending on schema and method of encoding and decoding, CHAN CODE therefore includes at least Content Code, and where appropriate plus Classification Code, and where appropriate or necessary plus other Indicator Code as contained in or mixed inside with the Content Code itself or contained in the Header, such as indicating for instance the Coding method or Code mapping table being used in processing a Super Processing Unit. This will be apparent in the description of the present invention in due course; up to here, CHAN FRAMEWORK contains the following elements: Code Unit,
• Rank and Position as well as the sum listed out in Paragraph [14] above, such relations are represented in the RP Piece and the CV Piece of CHAN CODE using the simplest mathematical formula, A+B in the CV Piece.
• the RP Piece simply contains 1 bit, either 0 or 1, indicating Bigger / Equal and Smaller in value of the first value a in relation to the second value b of the two Code Units read in one Processing Unit.
• a digital file of digital information or a section of the digital file (if the digital file is further divided into sections for processing) has to be broken down into one or more Processing Units or Super Processing Units for making each of the encoding steps, and the encoded code of each of the Processing Units or Super Processing Units thus made are elements of CHAN CODE, consisting of one RP Piece and one CV Piece for each Processing Unit, a unit of CHAN CODE in the present case of illustration.
• the digital file (or the sections into which the digital file is divided) of the digital information after compression or encryption using CHAN CODING therefore consists of one or more units of CHAN CODE, being the CHAN CODE FILE.
• the CHAN CODE FILE may also include, but not necessarily, any remaining un-encoded bits of original digital information, the Un-encoded Code Unit, which does not make up to one Processing Unit or one Super Processing Unit, together with other added digital information representing the header or the footer which is usually used for identifying the digital information, including the check-sum and the signature or indicator as to when the decoding has to stop, or how many cycles of encoding or re-encoding made, or how many bits of the original un-encoded digital information present in the beginning or at the end or somewhere as indicated by the identifier or indicator in the header or footer.
• Such digital information left not encoded in the present encoding cycle could be further encoded during the next cycle if required.
• This invention does not mandate how such additional digital information is to be designed, to be placed and used. As long as such additional digital information could be made available for use in the encoding and decoding process, one is free to make their own design according to their own purposes. The use of such additional digital information will be mentioned where appropriate for the purpose of clarifying how it is to be used.
• This invention therefore mainly covers the CHAN CODE produced by the techniques and methods used in encoding and decoding, i.e. CHAN CODING within CHAN FRAMEWORK.
• CHAN CODE could also be divided into two or more parts to be stored, for instance, sub-pieces of CHAN CODE may be separately stored into separate digital data files for the use in decoding or for delivery for convenience or for security sake.
• the CHAN CODE Header or Footer could also be stored in another separate digital data file and delivered for the same purposes.
• Files consisting such CHAN CODE and CHAN CODE Header and Footer files whether with or without other additional digital information are all CHAN CODE FILES, which is another element added to CHAN FRAMEWORK defined in Paragraph [14].
• CHAN CODE is the encoded code using CHAN CODING.
• CHAN CODING produces encoded code or derived code out of the original code.
• CHAN CODE represents the compressed code (if compression is made possible under the schema and method used), which is less than the number of bits used in the original code, whether random or not in data distribution. Random data over a certain size tends to be even, i.e. the ratio between bits 0 and bits 1 being one to one.
• CHAN CODE represents the result of CHAN CODING, and in the present example produced by using the operation specified by the corresponding mathematical formula(e), i.e.
• the RP Piece represents the indicator information, indicating the Rank and Position Characteristics of the two Code Units of a Processing Unit, produced by the encoder for the recovery of the original code to be done by the decoder. This indicator, specifying the rule of operation to be followed by the decoder upon decoding, is included in the resultant encoded code.
• the rule of operation represented by the mathematical formula, A+B could be embedded in the encoder and decoder because of its consistency and regularity of application in encoding and decoding.
• Derived components are components made up by one or more basic components or together with other derived component(s) after being operated on by certain rule(s) of operation such as represented by mathematical formula(e), for instance including addition, subtraction, multiplication or division operation.
• CHAN CODE obtained after the processing through using CHAN CODING, includes the digital bits of digital information, organized in one unit or broken down into sub-pieces, representing the content of the original digital information, whether random or not in data distribution, that could be recovered correctly and losslessly.
• the above example does not allow for correct lossless recovery of the original digital information. It requires, for instance, another mathematical formula, such as A minus B and/or one of the corresponding piece of Content Code to be present before the original digital information could be restored to.
• Another mathematical formula such as A minus B and/or one of the corresponding piece of Content Code to be present before the original digital information could be restored to.
• the above example is just used for the purpose of describing and defining CHAN FRAMEWORK and its elements so far.
• the components of the Compression Unit and their relations (3) compute, through applying mathematical formula or formulae designed, which describe the characteristics of or the relations between the components of the original digital information so obtained after the analysis of CHAN CODING, that the characteristics of the original digital data are represented in the CHAN CODE; if compression is made possible, the number of digital bits of CHAN CODE is less than the number of digital bits used in the original code, whether in random data distribution or not; the CHAN CODE being a lossless encoded code that could be restored to the original code lossless on decoding [using mathematical formula(e) and the associated mathematical operations in encoding does not necessarily make compression possible, which for instance depends very much on the formula(e) designed together with the schema and method used, such as the Code Unit Definition and the technique of Code Placement]; and (4) produce the corresponding CHAN CODE related to the original digital information read in step (1).
• What the CHAN CODING does for decoding the corresponding CHAN CODE back into the digital original code includes the following steps: (5) read in the corresponding CHAN CODE, (6) obtain the characteristics of the corresponding CHAN CODE, (7) apply in a reverse manner mathematical formula(e) so designed, which describe the characteristics of or the relations between the components of the original digital information so obtained after the analysis of CHAN CODING, to the CHAN CODE, including the use of normal mathematics and COMPLEMENTARY MATHEMATICS; (8) produce after using step (7) the original code of the original digital information lossless, whether the original digital information is random or not in data distribution. So on decoding, the CHAN CODE in Diagram 3 is restored correctly and losslessly to the original digital data code in Diagram 2.
• the resultant CHAN CODE could be regarded an encrypted code that could be used to recover the original digital code correctly and losslessly; the encrypted CHAN CODE so produced however may be an expanded code, not necessarily a compressed code.
• the method and the associated techniques for producing compressed code out of digital data whether random or not in distribution, putting an end to the myth of Pigeonhole Principle in Information Theory, will be revealed in due course later after discussing the inventive feature of novel Code Unit definition and other techniques used in implementing the novel features of CHAN FRAMEWORK.
• CC Complementary Constant or Variable, being a Constant Value or Variable Value chosen for the operation of COMPLEMENTARY MATHEMATICS, which is defined as using the Complementary Constant or Variable (it could be a variable when different Code Unit Size is used in different cycles of encoding and decoding) that is used in mathematical calculation or operation having addition and subtraction logic as explained in the present invention.
• CC Complementary Constant or Variable, being a Constant Value or Variable Value chosen for the operation of COMPLEMENTARY MATHEMATICS, which is defined as using the Complementary Constant or Variable (it could be a variable when different Code Unit Size is used in different cycles of encoding and decoding) that is used in mathematical calculation or operation having addition and subtraction logic as explained in the present invention.
• A is the value being operated on, the example used here is the Rank Value A, A being bigger or equivalent in value to B in the present case of using two Code Unit Values only; so in the first formula:
• a and B after separation could be restored correctly to the position of first value and the second value read as a and b.
• Step (2) just shows how COMPLEMENTARY MATHEMATICS works when operating on such basic
• COMPLEMENTARY MATHEMATICS does not directly help to meet the challenge of the Pigeonhole Principle in Information Theory. However it does highlight the concept of using range for addition and subtraction of data values and the concept of a mirror value given a Complementary Constant or Value. It is with this insight of range that the challenge of Pigeonhole Principle in Information Theory is met with successful result as range is essential in the operation of using Absolute Address Branching or latent in the way how data value or number is to be represented and defined.
• the four basic components of a Processing Unit could be arranged into 3 Arms, i.e. the Long Arm, the Middle Arm and the Short Arms, with 2 pairs of basic components, representing the Upper Corner (being the pair of the two basic components with a bigger sum) and the Lower Corner (being the pair of the two basic components with a smaller sum) of the respective arms.
• the values of these pairs happen to have same values in one way or anther, so that there may be less than 3 arms, such as only 2 arms or 1 arm or even becoming a dot shape. Therefore the distribution of the values of the four basic components of a Processing Unit could be represented in different CHAN SHAPES as follows:
• CHAN LINE 1 The three arms all overlap together with the Short Arm having values [l]+[4] being the Upper Corner and [2]+[3] being the Lower Corner.
• CHAN LINE 2 The three arms all overlap together with the Short Arm having values [2]+[3] being the Upper Corner and [l]+[4] being the Lower Corner.
• CHAN RECTANGLE 1 showing the incoming stream of data values of 4 Code Units one after the other in sequence
• the above CHAN RECTANGLE shows the first Code Unit Value a, of the Processing Unit is B, the second in ranking amongst the four Code Units; the second Code Unit Value b is C, the third in ranking; the third Code Unit Value c is A, the first in ranking; the fourth Code Unit Value d is D, the last in ranking.
• TRAPEZIUM 1 Lower Corners of the 3 arms are [3]+[4], [2]+[4] and [2]+[3].
• CHAN TRAPEZIUM 1 the values of the Long Arm, the Middle Arm and the Short Arm could be redistributed as follows:
• the Long Arm is always equal to or bigger than the Short Arm by 2*([2]-[4]) and the Middle Arm is always equal to or bigger than the Short Arm by 2*([3]-[4]).
• the Long Arm is always equal to or bigger than the Short Arm by 2*([l]-[3]) and the Middle Arm is always equal to or bigger than the Short Arm by 2*([l]-[2]).
• Short Arm overlaps with the Middle Arm with Upper Corner and Lower Corner of the Short Arm being [2]+[3] and [l]+[4] respectively. If the two arms therein are not equal in length, it is a trapezium, otherwise it is a square:
• the four values of the four basic components have to be represented by 1 CV Pieces consisting of 4 sub- pieces of values (produced by the use of four formulae designed for such purpose; one could attempt to make use of three or less formulae, so far the efforts do not appear to show promising results; one however should not rule out such possibility as there are plenty opportunities to introduce new techniques to CHAN FRAMEWORK as the present invention will show in this Application) in addition to the RP Piece, which is used to indicate the relationship between the Position and Rank of the values of the 4 basic components as shown in the following Diagram 8:
• CHAN RECTANGLE 3 showing the Ranking and Position of incoming stream of data values of 4 Code Units and the 64 bit size used
• One very distinguishing characteristic of the present invention is the varying bit sizes of values of the 4 sub-pieces making up the CV Piece; and RP Piece itself varies between 4 bit and 5 bit; and despite their varying bit sizes, CHAN CODING techniques to be revealed later could be used to decode the relevant CHAN CODE and restore it losslessly and correctly back into the original incoming digital data codes.
• the varying bit sizes used is intended for further raising the compression ratio through using CHAN CODING techniques over the compression ratio that could be achieved using mathematical formulae.
• RP Piece is to be explained here first.
• RP Piece is used for indicating the relative positions of the 4 Ranked Values of the four basic components, the four Code Units, of a Processing Unit because the Ranking of the four basic components may vary with their positions, there is no fixed rule for determining the relationship between position and ranking of the values of the four basic components.
• Diagram 9 Diagram 9
• Absolute Address Branching is therefore a design in which an address, instead of indicating one value as it normally does, now could branch to identify 2 or more values using extra one bit or more bits, depending on design. It is used when the range limit is known, i.e. the maximum possible combinations or options that a variable value is to choose from for its determination. For instance, in the above RP Table, it is known that there are only 24 combinations of Rank and Position, so the maximum possible combinations are only 24, because it is known it could be used as the range limit for indicating which particular value of the RP combination that a Processing Unit has, indicating how the values of [1], [2], [3] and [4] are to be put into the first, the second, the third and the fourth positions of the incoming digital data stream. Because this range limit is known and Absolute Address Branching is used, therefore on average, only four and a half bit is required instead of the normally five bits required for these 24 combinations.
• the 3 formulae used in the aforesaid PCT Application is designed in accordance to a positive thinking in order that using the 3 formulae, one is able to reproduce the associated CHAN SHAPES, including CHAN TRAPESIUM or CHAN SQUARE or CHAN TRIANGLE or CHAN DOT or CHAN LINE as the case may be. But it is found out that using this mind set, the basic components could not be separated out (or easily separated out because the combinations for calculation could scarcely be exhausted) from their derived components as expressed in the 3 formulae so designed using the techniques introduced in that PCT Application.
• COMPLEMENTARY CODING may be useful ones.
• Step (1) to Step (3) are:
• the RP Piece and the CV Piece are read out for decoding by using Absolute Address Branching technique and by looking up the retrieved value, the Rank Position Code of the corresponding Processing Unit against the relevant Rank Position Code Table used as in Diagram 9 to determine where the ranked values of [1], [2], [3] and [4] of the Processing Units are to be placed during decoding.
• the ranked values of [1], [2], [3] and [4] are determined as shown in the above steps outlined in Paragraph [38] using the values of the 4 sub-pieces of the corresponding CV Piece stored in Step (I) to Step (IV) in Paragraph [37].
• the 4 sub-pieces of the CV Piece are to be placed using the techniques revealed in Paragraph [43] and [44], which elaborate on the value of COMPLEMENTARY MATHEMATICS AND COMPLEMENTARY CODING in determining the range limit for the placement of the CV sub-pieces for adjustment of design where appropriate.
• Absolute Address Branching technique is technique for optimizing the space saving here. Simple substitution of a, b, c, d, replacing [1], [2], [3] and [4] in the four formulae as described in Paragraph [37] also indicates that the RP Piece could also be dispensed with. This means that, through such substitution, the formulae outlined in Paragraph [37] and [38] also work without RP processing. But without RP processing, the advantage of the possible space saving resulting from the use of range limits is then lost. That could result in more space wasted than using RP processing.
• COMPLEMENTARY MATHEMATICS AND COMPLEMENTARY CODING helps very much during making the design for the placement of the CV sub-pieces for space saving which may result in adjustment of the original formula design where appropriate.
• Diagram 10 below illustrates the contribution made by using COMPLEMENTARY MATHEMATICS AND COMPLEMENTARY CODING during the formula design phase in the present endeavor using the formula design in Paragraph [31] together with the following Diagram 10:
• X is not known by itself and merged as part of the formula: ([2] - [3]) + 1/2 ([3] - [4]).
• the anomaly or discrepancy or adjustment, 1 /2 ([3] - [4]), being introduced into these formulae mainly are introduced to the properly designed formulae of [3] + [4] and [2] - [3] describing neatly the associated CHAN SHAPE. Because the average of [3] + [4] is either ([4] + 1 2 ([3] - [4]) or ([3] - 1 2 ([3] - [4]), one could use either of which to introduce the anomaly or discrepancy or adjustment into it.
• the technique of introducing Formula Discrepancy or Formula Anomaly or Formula Adjustment includes the following steps: (i) designing formulae which could be used to reproduce the values or relations and characteristics of derived or basic components; (ii) finding what derived or basic components which are missing but essential for supplying additional values for the purpose of separating basic components out from the components represented by the formulae designed; (iii) designing formula anomaly or formula adjustment or formula discrepancy using formulae that could supply these missing components; such formula anomaly or formula adjustment or formula discrepancy is to be introduced into the formulae used to obtain values of the CV sub-piece(s) of CHAN CODE; (iv)
• the CC value of [4] - l/2([3] - [4]) is to be placed as the first CV sub-piece so that the second CV sub-piece represented by the formula of [1] - [4] could use the mirror value of (by making the CC operation on) [4] - 1/2 ([3] - [4]) as the range limit for storing the value of [1] - [4].
• [1] - [4] could be used as the range limit for ([2] - [3]) + 1/2 ([3] - [4]), this is because the mirror value of [2] - [3] using [1] - [4] as the Complementary Variable is [1] - [2] plus [3] - [4] and [3] - [4] should be more than 1/2 ([3] - [4]), so it is certain that ([2] - [3]) + 1 2 ([3] - [4]) lies within the range of [1] - [4].
• [1] - [4] could be put as the second CV sub-piece serving the range limit for the third CV sub-piece, ([2] - [3]) + 1/2 ([3] - [4]), for more bit storage saving.
• the range limit for placing the first CV sub-piece is the CC value as no other range limit is available before it as a reference. Also as for some rare cases where the value of [4] - 1/2 ([3] - [4]) could become negative, an extra sign bit has to be used for it. Also because the value could be with a fraction of 0.5 due to the halving operation, a fraction bit has also to be included for such indication. So altogether it is the CC bit size + 2 bits.
• the third CV sub-piece, ([2] - [3]) + 1/2 ([3] - [4]) may also have a value fraction of 0.5 because of the halving operation, so one more fraction bit has to assign above onto the range limit set by the value of [1] - [4].
• the placement of these 3 sub-pieces of CV Piece of the CHAN CODE could then be done for the Steps (1) to (3) in Paragraph [31] revealed above.
• the range limit used should be able to embrace all the possible values that could appear for which the relevant range limit is designed to be used.
• the range limit may require adjustment by adding the numerical value 1 to it; this is because the rank values are ranked according to the value itself and when being equal in value, they are ranked according to their positions in the incoming digital data stream.
• Formula (I) 3*([1] - [2] + [3] - [4]) + ([2] - [3]) + ([1] + [3]);
• Formula (II) 3*([1] - [2] + [3] - [4]) + ([2] - [3]) - ([2] + [4]);
• Formula (III) [3] - [4]; is estimated to be 5 Code Units, 3 Code Units and 1 Code Unit respectively.
• the RP Piece providing for 24 combinations uses up another 5 bits; if Absolute Address
• Branching is used, some combinations may just use up 4 bits. So if the Code Unit Size is taken to be 64 bits, then 68 bits, 66 bits and 64 bits are used for Formula (I), (II) and (III) respectively, without counting out the space optimization that could be achieved using Range Limiting. Using Range Limiting, it is obvious that the value of Formula (I) is bigger than that of Formula (II) and Formula (II) bigger than Formula (III). So Formula (I) should be placed first and then Formula (II) and then Formula (III). Using such placement technique, bit storage could be minimized.
• COMPLEMENTARY MATHEMATICS provides very useful concept and more technical tools for saving storage space.
• its importance lies rather in the paradigm it provides, including range processing, mirror value, as well as base shifting, for instance, the base for indicating the mirror value of a value is using the CC value, i.e. the Code Unit Size, as the base for counting reversely instead of the base of Value 0 when doing normal mathematical processing.
• COMPLEMENTARY MATHEMATICS AND COMPLEMENTARY CODING helps in the formula design phase and in encoding and decoding. So CHAN MATHEMATICS AND CHAN CODING is a super set of mathematical processing including normal mathematics and COMPLEMENTARY MATHEMATICS used in conjunction or alone separately with reference to CHAN SHAPES and the characteristics and relations so revealed in making encoding and decoding of digital information, whether in random or not.
• decompression algorithms and process could be designed and implemented.
• the number of cycles of encryption / decryption and compression / decompression also has effects on the outcome code. And if such information, including the formulae designed and the number of cycles of the encryption / decryption and compression / decompression implemented, is sent separately from the data intended to be sent, data security could be enhanced and greatly protected on an unprecedented level.
• CHAN CODE could be separately stored and sent out in the correct order for recovery of the original digital information; such as the sign bits for the CV sub-pieces being in one sign bit file, each CV sub-piece being in a separate CV sub-piece file, the RP Pieces being in a RP Piece file, and the header or footer containing additional information relating to the processing of the corresponding CHAN CODE being in a separate header or footer file.
• CHAN FRAMEWORK is characterized by the following structural features:
• Code Unit including content codes and classification codes
• CHAN FILES digital data files containing CHAN CODE made up of the digital code of the above (a) to (g) in combination or alone).
• CHAN FRAMEWORK refers to the definition chosen for any of the above structural elements, if used, in combination under different
• Code Unit is the basic unit of CHAN FRAMEWORK.
• its size i.e. Code Unit Size
• Code Unit Size is measured in number of binary bits (bit size) and the maximum number of values (Code Content) that a Code Unit can represent is therefore limited by the bit size of the Code Unit under a conventional binary data coder (a data coder, especially data coder where all its unique values are having the same bit size, not having the features of data coder as designed under CHAN FRAMEWORK as revealed in the present invention).
• bit size i.e. Code Unit Size
• Code Content code Content
• Code Unit has the bit size of 3, then it can represent at most 8 bit values, namely 000, 001, 010, 011, 100, 101, 110, and 111. This is the conventional way of using binary bits to represent data values.
• Code Unit is the basic unit of data that is read in one by one from the data input stream by the encoder for encoding purpose. It is this conventional way of reading and representing data which gives rise to the myth of Pigeonhole Principle in Information Theory, details of which could be found at: http s : //en . wi ki pedi a. org/wiki /Pi geonhol e_pri ncipl e
• the Code Unit for encoding here, if the Code Unit of bit size of 3 bits, it could only provide 8 addresses and so it could only be used to represent at most 8 unique values, one value at an instance of time.
• the number of addresses that a Code Unit can have is measured in binary bit size, the bigger the number of binary bits used for a Code Unit, the more addresses that the Code Unit can have for representing Code Content values in one one correspondence. So the number of addresses that a Code Unit has is equal to 2 to the power of the bit size (the number of binary bits) of the Code Unit, i.e. the number of binary bits measuring the size of the Code Unit.
• Random data tends to be even in the ratio between the number bit 0 and bit 1 where bit 0 and bit 1 are appearing in a random way, i.e. without any regularity or predictable pattern revealed so far. So it is long held that random data could not be compressed, giving rise to the myth of Pigeonhole Principle in Information Theory.
• FRAMEWORK provides a way of describing digital data of all types of distribution, including random distribution, more characteristics and their regularity of random data could be investigated and revealed, thus with the introduction of the concept and the use of the Super Processing Unit together with data coder holding unique code unit values not using the same bit size and other CHAN CODING techniques, such as Exception Introduction and especially DIGITAL D ATA BLACKHOLING with the use of Absolute Address Branching or Address Address Multiple Branching under CHAN
• Code Unit under CODE FRAMEWORK is firstly measured by the maximum number of unique Code Values that a Code Unit is used to represent or hold, secondly by the number of binary bits of the whole Code Unit (affecting the bit size possible of individual unique Code Values), and thirdly by the Head Design of the Code Unit Definition, where appropriate, as will be seen in Diagram 14 of Paragraph [62] below.
• Code Unit changes from 3 -bit Code Unit to 8-value Code Unit (or Max8 Code Unit), using the maximum number of unique Code Values that a Code Unit is used to hold as the first or primary factor to name or represent (of course one at a time) the Code Unit rather than the number of bits, which could then be used as the secondary factor, for distinguishing the size of a Code Unit.
• This also means that the individual unique Code Values of a Code Unit could be different in bit size in addition to the conventional definition that all the unique Code Values of a Code Unit could only be represented in the same bit size.
• this novel feature does not prevent one from designing a schema using a standard bit size for all the values of a Code Unit, it only provides the opportunity for designing schema using different bit sizes for different unique Code Values of a Code Unit in addition to the conventional definition. That means, the different unique Code Values of a Code Unit could have different bit sizes; and in addition, it also allows for giving each of the unique Code Values of a Code Unit the same number of bits in size, depending on the Code Value Definition and the related Code Unit Definition used at a certain time of encoding and decoding processes under a specific schema and design of encoding and decoding. For instance, for a 8-value Code Unit, all the 8 unique Code Values could be defined having the same bit size of 3 bits under a specific schema and design such as in Diagram 11 :
• Code Values of a Code Unit could have the same bit size or have different bit sizes, such option depending on how it is defined under a specific schema and design used for encoding and decoding.
• Such Code Value Definition or Code Unit Definition could also change where necessary and appropriate in the course of encoding and decoding, using the code adjustment technique of CHAN CODING.
• Code Unit Size is just measured in terms of bit size, such as 1 bit Code Unit, 2 bit Code Unit, so on and so forth. This is not true when Code Unit could be measured in terms of the maximum number of Code Values that a Code Unit is designed to hold.
• the conventional way of measuring Code Unit in terms of the number of binary bits puts up a restriction that the number of Code Values that a Code Unit could hold is determined by the number of binary bits used for a Code Unit; for instance, a 3 -bit Code Unit could hold at maximum 8 unique Code Values, each using 3 bits to represent, no more and no less.
• a 3 -bit Code Unit could not hold more than 8 unique Code Values. What is more, when reading data, using this conventional definition, the encoder or decoder could not avoid reading all the 8 unique Code Values if they are present there; that means, the encoder or decoder could not say just read 3 unique Code Values and disregard or discard the other 5 unique Code Values if they are present in the data set. That means using the conventional Code Unit Definition, the associated coder would always process data sets using Code Values of the same bit length or bit size, no shorter or no longer than the bit size used in the Code Unit Definition. This restriction is removed under CHAN FRAMEWORK.
• the number of Code Addresses available is by design exactly the same as the number of Code Values that the Code Unit is designed to hold. So if all the unique Code Values appear in the data set, all the Code Addresses are exhausted so that compression of a random data set could not be made possible by techniques only capitalizing on unevenness in the frequency distribution of the Code Values present in the data set (except for the use of CHAN CODING); as for a random data set, such frequency distribution for all the Code Values of the data set tends to be even, i.e. the ratio between bit 0 and 1 of the whole data set is 1 to 1, and the frequency of all the Code Values of the Code Unit is about the same.
• Diagram 13 shows the design for a 3 -value Code Unit, Max3 Code Unit, using the novel feature (i.e. Code Unit being measured by the maximum number of Code Values; the number of binary bits is used as a secondary measurement for the Code Unit as a whole) just introduced into CHAN FRAMEWORK:
• 3 -value Code Unit definition Two versions of design for 3 -value Code Unit definition are meant for illustrating that more number of Code Addresses could be created for the number of unique Code Values that a Code Unit is designed for, thus providing more addresses than the number of unique values appearing in the data set.
• a schema of using a Processing Unit made up of three 3 -value Code Units is designed for use for encoding and decoding a digital data input stream for making data compression.
• the Code Units of the digital data input stream is read one by one and 3 adjacent Code Units are encoded (or decoded for restoration afterward) as one Unit, the Processing Unit, using the definition of 0 Head Design; what the encoding or decoding does is reading three 3-value Code Units (reading three one by one) by using the Code Unit definition of 0 Head Design as Reader and then treat the code of the three Code Units as one piece of code (code of one Processing Unit) and change it with another piece of code, for instance, using the Code Unit definition of 1 Head Design as Writer to encode it or write it upon encoding; or restore it to the original code upon decoding by reading the encoded code with the 1 Head Design Code Unit definition and writing it back with the 0 Head Design Code Unit definition; or using mapping tables of other design for encoding or decoding. Because there are 3 unique Code Values of a Code Unit used here, a Processing Unit is designed to hold at maximum 27 unique values (3 values times 3 Code Units equal to 27 unique values) for representation. The number of addresses that is available
• 16bit Group 2-pair No Skew Single Branching with 2 No Skew versions of equal bit 0 to bit 1 ratio, both having bit 0 to bit 1 ratio as 8:8 (No Skew Distribution)
• 17bit Group 1-pair Single and 1 Multiple Branching with 2 versions, one having bit 0 to bit 1 ratio as 6: 11 and the other 11 :6
• 18bit Group 1-pair Single and 1 Multiple Branching with 2 versions, one having bit 0 to bit 1 ratio as 6: 12 and the other 12:6
• Code Definition schema under CHAN FRAMEWORK allows a Code Unit Definition having many different versions of definition, varying in Code Unit total bit size, varying in Code Unit values bit size, and varying in the number of unique values that the Code Unit is designed to hold, as well as varying in the 0 Head or 1 Head Design.
• Diagram 14c provides 2 No Skew versions (i.e. 0 Head Design and 1 Head Design) of 16-bit 6-value Code Unit.
• the 0 Head Design version is used for the discussion hereafter except where mentioned otherwise specifically.
• the No Skew version and the 3 -pair Skewed Single Branching version both use 16 bits for representing the 6 unique values of the 6-value Code Unit; they differ only in the pattern of bit codes used and the ratio between bit 0 and bit 1, with the No Skew version having the ratio as 8:8 and the 3-pair Skewed Single Branching version 7:9. So one could do a cross mapping between these 2 sets of 6 Code Values in order to increase, say, the number of bit 1 of the No Skew version, so that the ratio of bit 0 to bit 1 of the new data set after mapping translation from 8:8 to a ratio towards the 7:9 side.
• Diagram 15 gives one instance of result generated by running the autoit program given the PCT Application, PCT/IB2016/054732 filed on 22 February 2017, (as such autoit programs have be listed in this PCT Application under priority claim, one could gain access to them by making reference to the aforesaid PCT Application, and thus will be not listed in the present PCT Application anymore; however the program serving as the final proof that random data set could be subject to compression will be listed when discussing its use together with the autoit program library help file so that people skilled in the art could see how data coder for making encoding and decoding could be constructed for use for the purposes of making encryption/decryption and compression/decompression in actual implementation of CHAN FRAMEWORK with the use of methods and techniques of CHAN CODING in making CHAN CODE and
• Diagram 15 is just one instance of such generations only. Running the autoit program generating it once will generate one such instance, each instance will differ from other instances a little. But in general, such instances of the frequency distribution of the 6- value Code Unit maintains roughly the same proportions each time for the 6 unique Code Values under concern.
• Cross mapping between the Code Values of the No Skew version and the 3 -pair Single Branching version of the 6-value Code Unit and the related calculation is shown in Diagram 16:
• the ratio of bit 0 : bit 1 could be altered tilting towards one direction using the techniques outlined in Paragraphs [62] to [64] above or [115] and [116] below, then depending on the data distribution, one could use the cross mapping technique of code values for making compression, and this time using cross mapping of Code Values of Code Units of the same value size but of different bit sizes, for instance in the example now being used: 6-value Code Units, having different bit sizes, such as reading the data set using 6-value Code Unit of 20 bit size (or any other bit sizes where appropriate) and cross mapping such Code Values with those Code Values of 6-value Code Unit of 19 bit size (or any other bit sizes where appropriate) for encoding purpose, depending on the frequency distribution of the Code Values of the data set under processing.
• Code Unit Size could now be measured by the number of Code Values as well as by the number of binary bits as illustrated by the examples given in Diagram 14 for 6-value Code Values having different bit sizes, other characteristics of the data set could also be investigated and found out, such as the ratio of bit 0 to bit 1 and the frequency distribution of the unique Code Values of Code Unit for any Code Unit Definition with a certain number of values and a certain bit size. This facilitates the description of any digital data set as well as the use of appropriate techniques for encoding and decoding for any purposes, including the purposes of making data encryption and data compression together with correct and lossless recovery of the original digital data.
• Processing Unit (the unit for encoding or for writing of a piece of encoded code) could be made up by only 1 Code Unit as Diagram 14 shows that a Code Unit having the same number of Code Values could be designed to be having different bit sizes for each of the code values and for the Code Unit as a whole. So a Code Unit, i.e. the basic Read Unit, could by itself be used alone without having to combine with other Read Unit(s) to form a Processing Unit, the basic Write/Read Unit, for writing encoded code in the encoding process and for reading back during the decoding process.
• Identifying and organizing traits or characteristics of Code Units, either in single or in combination, for producing Classification Code of CHAN CODE is one such technique, such as producing RP Code using the rank and position of Code Units or designing mathematical formulae that could be used to describe Code Values of Code Units either in single or in combination, and that could also be used in encoding and decoding purpose, for instance for creating Content Value Code, the CV sub-pieces, of CHAN CODE. So the basic part of CHAN CODE (the part that describes the traits or characteristics of Code Units) under CHAN FRAMEWORK could be divided into Classification Code and Content Value Code (or Content Code in short). Other parts that could be regarded belonging to CHAN CODE include other
• identification code or indicators for instance included in main Header for CHAN CODE FILES or in section header for sections of a digital data file) for identifying the cross mapping table (Mapping Table Indicator) used for encoding and decoding the basic part of CHAN CODE, the number of cycles (Number of Cycle Indicator) of encoding and decoding for a particular digital data input, the checksum (Checksum Indicator) calculated for CHAN CODE FILES, the Un-encoded Code Unit of the digital data for any particular cycle of encoding and decoding if any, as well as other indicators which are designed by designer for use for the purposes of identifying as well encoding and decoding CHAN CODE where appropriate and necessary.
• One such indicator for instance could be the number of Processing Units making up a Super Processing Unit for use in encoding and decoding; others could be indicator for adjustment of Classification Code of CHAN CODE by frequency and indicator for adjustment of Content Code of CHAN CODE by frequency where appropriate and desirable (i.e. Frequency Indicators for adjustment of using 0 Head or 1 Head Design for Classification Code and for Content Code as appropriate to the patten of Bit 0 : Bit 1 ratio of the digital data set under processing, Frequency Indicators in short).
• the concept and usage of Super Processing Unit and of the adjustment of CHAN CODE by frequency will also be revealed later.
• CAABCT Classified Absolute Address Branching Code Table
• PU Bit Representation in CHAN CODE including Class Bit, Normal Bits and Branch Bit
• Example I Classified Absolute Address Branching Code Table
• the 27 Code Values of three 3 -value Code Units of a Processing Unit could be cross mapped one by one into CHAN CODE, including the Class Bit (Classification Code), and the Normal Bits & Branch Bit (Content Code).
• Class Bit Classification Code
• Constent Code Normal Bits & Branch Bit
• Tablel size is the bit size resulted from cross mapping between the 27 unique code values of Diagram 21 sorted in bit usage (such a sorting of the 27 unique code values is listed in Diagram 23 in Paragraph [78] below) and the 27 unique codes found in the Classified Absolute Address Branching Code Table (CAABCT) For 27 Values used in Example I as listed out in Diagram 18 of Paragraph [73].
• CAABCT Classified Absolute Address Branching Code Table
• CAABCT Classified Absolute Address Branching Code Table
• PU Bit Representation in CHAN CODE including Class Bit, Normal Bits and Branch Bit
• Diagram 21 The random data set generated and listed in Diagram 21 and read up using the aforesaid 3 counts of 3 -value Code Units of 0 Head Design takes up 80001 bits and the bit usage by encoding that random data set so read using cross mapping with table codes of the CAABCT in Example II (Table2a in Diagram 23) is therefore the same: 80001 bits.
• the CAABCT in Example II uses up 135 bits for all its 27 unique table codes in 1 count each; the CAABCT in Example I uses up only 130 bits.
• the CAABCT in Example I uses 130 bits for an even frequency distribution of 1 count each for its 27 unique table codes
• the CAABCT in Example II uses more than the CAABCT in Example II (using 135 bits for an even frequency distribution of 1 count each for its 27 unique table codes) in terms of bit usage when encoding the original random data set of 8,0001 bits, producing an encoded code using 8, 1989 bits instead as seen in Diagram 23, an expansion rather than compression.
• Table2a being the cross mapping result using CAABCT 2, Table2b CAABCT 1, and Table3 CAABCT 0 as discussed in Paragraphs [85] to [93] and Diagram 29) is listed out in Diagram 21 and extracted as below:
• the whole digital data input file could be regarded a Huge Processing Unit consisting of all the Processing Units of the digital data at a certain point of the data distribution spectrum, from random or even to wholly uneven at either extremes.
• compression techniques are possible just through taking advantage of the uneven nature of a data set. And a data set of random distribution so far is considered incompressible.
• a single Huge Processing Unit consisting of Processing Units of random data as a whole could be divided into sub-sections consisting of a certain number of Processing Units called Super Processing Units, so that techniques could be designed for compressing such data sub-sections.
• So Huge Processing Unit is defined as the whole unit consisting of all the data codes that are to be put into encoding and decoding, therefore excluding the Un-encoded Code Unit, which is made up by data codes that are not subject to the process of encoding and decoding, for instance, because of not making up to the size of one Processing Unit or one Super Processing Unit where appropriate.
• a Huge Processing Unit could be divided into a number of Super Processing Units for encoding and decoding for the sake of a certain purpose, such as compressing random data through such division or other purposes.
• the encoding and decoding of data for a Super Processing Unit may require some adjustment made to the encoding and decoding techniques or process that are used by encoding and decoding made for a Processing Unit. Therefore, a Super Processing Unit is a unit of data consisting of one or more Processing Units. It could be subject to some coding adjustment to the encoding and decoding made for a Processing Unit.
• each of the code values within a particular group may slightly vary from one random data set to another random data set because of the slight variation in frequency distribution of random data generated from time to time. But code values will not move from one group to another in terms of their frequencies between one instance of random data to another instance. If they do change so wildly, the data distribution is not random at all.
• the frequency ranking of the data code values of 27 unique code values under concern may be different from that of a random data set. So the order of such 27 unique code value frequencies must be known so that cross mapping of table codes of CAABCT and the 27 unique code values could be designed so as the best result for compression is to be attempted. So such an order of the unique code value frequencies should be obtained by parsing the data set under concern first and such information has to be made available to the encoder and decoder for their use in processing. Such information could vary from one data set to another data set so that it could be included in the Header of the encoded code for use later by decoder for correct recovery of the original data set.
• CAABCT is used here because AAB technique is used in designing the mapping code table for the 27 unique code values of the Processing Unit using three 3 -value Code Unit of 0 Head Design. So other mapping code tables without using AAB technique could also be designed for use where appropriate. So the mentioning of CAABCT for use in the present case of discussion applies to the use of mapping code table in encoding and decoding in general.
• Super Processing Units that have equal or less number of processing units than a full set of processing units (in the present example 27 unique entries of data values) are guaranteed to have an uneven data distribution. However, it does not mean that all uneven sub-sections of data are compressible. This is so since any compression technique or mapping code table that is useful in compressing data of a certain data distribution may not suit to data of another different data distribution. This means that more than one compression technique or one mapping code table has to be used in compressing Super Processing Units of different data distribution.
• the first attempt is to classify the Super Processing Units into two groups, using one CAABCT for encoding and decoding the Processing Units of Super Processing Units of one group and another CAABCT for another group.
• one bit indicator about which CAABCT is used for either of the two groups has to be used for one Super Processing Unit. So additional bit usage has to be incurred for making compression using this approach.
• the encoding implemented using the relevant CAABCTs for making compression should result in bit usage saving that is more than the bit usage that has to be incurred by using the
• CAABCT use of CAABCT (two for the present case) for cross mapping between unique data code values and unique table code values (of the two groups of Super Processing Units) and use of CAABCT indicator.
• Processing Unit made up of 27 Processing Units or less should meet this criterion as 27 unique code values if all present or not do not constitute a random data set of Code Unit designed in conventional sense using fixed bit size.
• a random data set of Code Unit designed in conventional sense using fixed bit size when read using the schema and design of Processing Unit made up of three 3 -value Code Units of 0 Head Design exhibits a characteristic data frequency distribution that is shown in Diagram 23 other than the one count for each of the 27 unique values shown in Diagram 18.
• Using a fixed size Super Processing Unit could be one way to accomplish subdivision. So for the time being a Super Processing Unit is considered having the size of 27 Processing Units first.
• a Super Processing Unit having the size of 27 Processing Units here do not guarantee each of the unique 27 code values will be present in each of the Super Processing Units so divided.
• each may have a different data distribution, some having all the 27 unique code values present, some having some unique code values absent while other unique code values occurring more than once, all in different ways. So for simplicity, the example here divides such different data patterns into two groups for encoding and decoding purpose.
• the statistics of bit usage and frequency distribution of a random data set of 80000 bits in Diagram 23 is refined in Diagram 24 as follows: Diagram 24
• AI Artificial Intelligence
• HI Human Intelligence
• a code value (Identifying Code Value) present in the Super Processing Unit that could be used for identifying which CAABCT is used for its encoding; so taking into account of this criterion, such a code value should be encoded in different table code values by the two different CAABCTs; and this requirement has to be catered for during the stage of designing the two CAABCTs under concern; also because of this requirement, the Terminating Condition or Criterion for stopping the use of one mapping code table for encoding a Super Processing Unit is to be changed; for instance at first it is taken that the size of the Super Processing Unit is to be 27 processing unit code values, and as the Identifying Code Value may not always be found amongst the 27 code values present in a Super Processing Unit, so the Terminating Condition has to be modified to: either
• Terminating Condition means that if from the head of the digital data input, only the third Super Processing Unit (of 27 code values in this case) contains the Identifying Code Value, then all the code values of the first 3 Super Processing Units are to be encoded using one CAABCT upon assessment, and a new assessment is to be made about using which CAABCT for encoding the code values ahead up to all the values of the Super Processing Unit containing the Identifying Code Value; and at the end, the last section of the original code values not making up to one Super Processing Unit with or without the Identifying Code Value could be processed in way like that in (i) above or just left as included in the Un-encoded Code Unit;
• CAABCT 0 there is only 1 trio whereas in CAABCT 1, there are 6.
• CAABCT 0 the trio is in 0 Head Design, that is having suffix in the form of:
• CAABCT 1 could be redistributed for cross mapping purpose as follows in Diagram 28:
• CAABCT 2 is exactly the same as CAABCT 1 except that:
• CAABCT 2 uses the 0 Head Design for its 6 trios (i.e. 0, 10, 11) whereas CAABCT 1 uses the 1 Head Design (i.e. 1, 01, 00) for their respective suffix to the trios;
• CAABCT 2 is used to cross map the data code values of the random data set for encoding; i.e. the random data set is read using the definition of the 3 -value Code Unit of 0 Head Design one by one, three of such consecutive Read Units form one Processing Unit for using with CAABCT 2 as a mapping table for encoding.
• the Processing Unit is then encoded one by one as well as the Super Processing Units as described above.
• CAABCT 1 is then used with Super Processing Units sub-divided from the translated data set using the chosen Terminating Condition, such as the original code value of 000, which is now translated into 010, the corresponding table code value of CAABCT 2.
• the Super Processing Unit under processing is susceptible to encoding using CAABCT 1 for producing encoded code which is less in bit usage than the translated code of the same Super Processing Unit, it is encoded by using CAABCT 1.
• the Terminating Condition includes the encoded CAABCT table code value of 010, if CAABCT 1 is used to encode it, 010 is encoded into 011. So the resultant encoded code after encoding using CAABCT 2 and CAABCT 1, the original data code value 000 is translated into 010 and then 011. If using CAABCT 1 could not reduce the size of the CAABCT 2 encoded code of the Super Processing Units, the CAABCT 2 encoded code values of those Super Processing Units are then left un-touched. So the original data code value 000 remains as 010.
• CAABCT 1 code is then decoded back into CAABCT 2 code for those Super Processing Units just identified.
• CAABCT 2 code After all CAABCT 1 code is translated back into CAABCT 2 code, cross-the-board decoding of CAABCT 2 code to the original data code values could be achieved using the code table of CAABCT 2. In this way, it could be asserted that whenever there are Super Processing Units having code values that are subject to compression by using CAABCT 1, then the random data set containing such Super Processing Units could be compressed.
• CAABCT 0 for cross mapping with CAABCT 2 instead of using CAABCT 1
• CAABCT 0 and CAABCT 1 interchangeably for cross mapping with CAABCT 2 where appropriate; in these cases, the AI criteria may have to be duly adjusted or added to for determining which mapping code table is used for any particular Super Processing Unit.
• Diagram 29 below shows the cross mapping that could be done using all 3 CAABCTs:

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